Geodesic
Minimal branches of solutions of nonlinear operator equations in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 113-119.

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We consider the nonlinear equation $B(\lambda)x=R(x,\lambda)+b(\lambda)$, where $R(0,0)=0$, $b(0)=0$, the linear operator $B(\lambda)$ has a bounded inverse operator for $S\ni\lambda\rightarrow0$, and $S$ is an open set, $0\in\partial S$. We examine the problem on the existence of a small continuous solution of the maximal order od smallness $x(\lambda)\rightarrow0$ as $S\ni\lambda\rightarrow0$. A constructive method way of constructing this solution is presented.
Keywords: nonlinear operator, Banach space, operator equation, minimal branch. 
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R. Yu. Leontiev. Minimal branches of solutions of nonlinear operator equations in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 113-119. http://geodesic.mathdoc.fr/item/INTO_2020_183_a9/

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